A generalized concept of interference suppression is introduced for multiuser systems with a known memoryless transmit non-linearity, such as in the downlink amplifier of a satellite communication system. By considering the operation of commonly used multiuser detection techniques from a viewpoint of constellation structure, we extend these notions to nonlinear multiuser systems. We also analyze the performance of such multiuser detectors in terms of their asymptotic multiuser error exponents, which reduce to the asymptotic multiuser effective energies for the respective detectors in the absence of nonlinearity. The asymptotic conditional error exponent is introduced as a quantitative measure for evaluating nonlinear multiuser detectors based on the conditional probability of error at high signal-to-noise ratio (SNR). The optimal affine detector that maximizes the asymptotic error exponent for a given user is derived along with a successive interference annulment (SIA) scheme that maxi...